Tree-based methods are popular nonparametric tools in studying time-to-event outcomes and are frequently used in studies with censored survival time. Interval-censored data, in which the event time is only known to lie in sometime interval, arise commonly in practice, for example, in a medical study in which patients visit clinics or hospitals at prescheduled times and the events of interest occur between visits.Such data are appropriately analyzed using methods that account for this uncertainty in event time measurement. In this thesis, we propose a survival tree method for interval-censored data based on the conditional inference framework. Using Monte Carlo simulations, we find that the tree is effective in uncovering underlying tree structure, performs similarly to an interval-censored Cox proportional hazardsmodel fitwhen the true relationship is linear, and performs at least as well as (and in the presence of right-censoring outperforms) the Cox model when the true relationship is not linear. Further, the interval-censored tree outperforms survival trees based on imputing the event time as an endpoint or the midpoint of the censoring interval. In this thesis, we introduce a novel framework for survival trees and ensembles, where the trees partition the dynamic survivor population and can handle timedependent covariates. Using the idea of randomized tests, we develop generalized time-dependent receiver operating characteristic (ROC) curves for eva‎luating the performance of survival trees. The tree-building algorithm is guided by decisiontheoretic criteria based on ROC, targeting specifically for prediction accuracy. Extensive simulation studies are conducted to examine the performance of the proposed methods. We apply the methods to a study on AIDS for illustration. Their structure and ease of interpretability make them useful to identify prognostic factors and to predict conditional survival probabilities given an individual’s covariates. The existing methods are tailor-made to deal with a survival time variable that is measured continuously. However, survival variables measured on a discrete scale are often encountered in practice. The authors propose a new tree construction method specifically adapted to such discrete-time survival variables. The splitting procedure can be seen as an extension, to the case of right-censored data, of the entropy criterion for a categorical outcome. The selection of the final tree is made through a pruning algorithm combined with a bootstrap correction. The authors also present a simple way of potentially improving the predictive performance of a single tree through bagging. A simulation study shows that single trees and bagged-trees perform well compared to a parametric model. A real data example investigating the usefulness of personality dimensions in predicting early onset of cigarette smoking is presented.

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